Complex Networks on Hyperbolic Surfaces

TL;DR

This paper introduces a new approach to generate and analyze complex networks through their embeddings on hyperbolic surfaces, revealing relationships between network properties and surface topology.

Contribution

It presents a novel method for network generation and classification based on hyperbolic surface embeddings, offering insights into network complexity and hierarchy.

Findings

Strong correlation between network properties and embedding surface topology

Hierarchical properties are shared among networks with similar embeddings

Local elementary moves explore network ensembles with common features

Abstract

We explore a novel method to generate and characterize complex networks by means of their embedding on hyperbolic surfaces. Evolution through local elementary moves allows the exploration of the ensemble of networks which share common embeddings and consequently share similar hierarchical properties. This method provides a new perspective to classify network-complexity both on local and global scale. We demonstrate by means of several examples that there is a strong relation between the network properties and the embedding surface.